Notice period during probation period - how to successfully leave my current employer?

Hello, I joined the company in the last week and now I am holding an offer from a good company and I want to resign, but in the offer letter they do not mention the notice period for the probation period.

Official notice period is 3 months. Could you kindly assist me in figuring out how to successfully leave my current employer?

You may better talk to the reporting officer, HOD and others and get relieved from service peaceably. Since it is a very limited period of service for a week you may agree to forego all salary.
If there is no mention of a notice period during probation, it would mean the 3-month rule would apply. I hope they did not make you a member of PF Scheme.